The author writes: "Presently traditional ways to determine signal spectra are based on the expansion of functions in Fourier series or on their representation by Fourier integrals with applying a system of basis ORTHOGONAL functions. For the first time, a new method of spectral analysis and approximation of analog and discrete signals of limited length is proposed. For this purpose, new concepts are introduced: finite spectrum (FSS) and entire spectrum (ESS) of a process segment that contain a limited and infinite harmonic set, correspondently. Notice, that the requirement of mutual ORTHOGONAL property is NOT IMPOSED on the harmonic sets. Spectrum calculation algorithms suitable for new method practical realization are offered." Available in Russian and English.